Question: Simplify the following expression: $a = \dfrac{48x^2 + 120x}{60x^2 - 156x}$ You can assume $x \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $48x^2 + 120x = (2\cdot2\cdot2\cdot2\cdot3 \cdot x \cdot x) + (2\cdot2\cdot2\cdot3\cdot5 \cdot x)$ The denominator can be factored: $60x^2 - 156x = (2\cdot2\cdot3\cdot5 \cdot x \cdot x) - (2\cdot2\cdot3\cdot13 \cdot x)$ The greatest common factor of all the terms is $12x$ Factoring out $12x$ gives us: $a = \dfrac{(12x)(4x + 10)}{(12x)(5x - 13)}$ Dividing both the numerator and denominator by $12x$ gives: $a = \dfrac{4x + 10}{5x - 13}$